If a metallic circular plate of radius 50 , c | vedclass

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(B) Let $A$ be the area of the circular plate and $r$ be its radius. The area is given by $A = \pi r^2$. Given that the radius $r = 50 \, cm$ and the

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$10$

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(B) Let $A$ be the area of the circular plate and $r$ be its radius. The area is given by $A = \pi r^2$. Given that the radius $r = 50 \, cm$ and the rate of change of the radius is $\frac{dr}{dt} = 1 \, mm/hour = 0.1 \, cm/hour = \frac{1}{10} \, cm/hour$. Differentiating the area formula with respect to time $t$,we get $\frac{dA}{dt} = 2\pi r \frac{dr}{dt}$. Substituting the given values,$\frac{dA}{dt} = 2 	imes \pi 	imes 50 	imes \frac{1}{10} = 10\pi \, cm^2/hour$. Thus,the rate at which the area of the plate increases is $10\pi \, cm^2/hour$.

If a metallic circular plate of radius $50 \, cm$ is heated so that its radius increases at the rate of $1 \, mm$ per hour,then the rate at which the area of the plate increases (in $cm^2/hour$) is (in $\pi$)

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